Arguably the biggest issue with Ancient Greek science, an approach that spread its way through most of the medieval period, was the dependence on authority. Just as we still do in law cases, most classical natural philosophy was decided by argument rather than by experiment or analysis. If someone repeatedly won the argument on a topic they were regarded as an authority and in some cases - Aristotle is the most obvious example - considered a source of wisdom on pretty well everything as a result. Hence the infamous suggestion that women had fewer teeth than men because Aristotle said it was so, and no one bothered to check. (Actually I am sure plenty did check and found it to be wrong, but because they weren't Aristotle, they were ignored.)
This reverence for the word of Aristotle was shattered in science itself by the likes of Galileo and Newton, and thereafter it should not be good enough just to be an authority figure to be assumed correct on any topic. But it tends to still happen outside of science. A good example today of when we make a mistaken appeal to authority is when, for instance, we think that a Nobel Prize winning scientist has more weight outside their specialist field than do other people. There is no reason, for instance, to give weight to Linus Pauling's beliefs on the medical benefits of vitamin C, because it wasn't his area of expertise - but still people do.
However, this is quite different from preferring people with expertise as sources within their subject of expertise to a random person on the street. That is not an appeal to authority, it is just common sense. I'm not a scientist, I'm a writer with a very rusty physics degree, and a very slightly less rusty operational research masters. As such, I would never dream of putting forward my own theories in science. But if I want to describe a physical theory or idea, I will give more weight to the word of a well-established physicist than I would to the next person who sends me their new physics theory by email.
I get sent quite a lot of these off-the-wall physics theories. I would not use those in one of my books, except to raise an eyebrow at it. Instead I put across ideas coming from well-established physicists (if I'm writing about physics - not if I'm writing about health). This is not using an appeal to authority, it's the only sensible thing to do as I can't possibly test out or check their theories myself. However, if I used Richard Feynman's viewpoint to provide expertise on music or Niels Bohr on literature, then I would indeed be incorrectly appealing to authority. Which would be wrong (as anyone who knows what Feynman's taste in music was would probably agree).
In the case that started this piece off, I had referenced another famous physicist George Gamow on a physics matter, so this was not the case. It's easily done, but we shouldn't confuse a flag that we are accessing expertise with an appeal to authority.